Chapter 6.1, Problem 39E

New York City 10-km Run. As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. Let x denote finishing time for finishers in this race.

1. a. Sketch the distribution of the variable x.
2. b. Obtain the standardized version, z, of x.
3. c. Identify and sketch the distribution of z.
4. d. The percentage of finishers with times between 50 and 70 minutes is equal to the area under the standard normal curve between ________ and ________.
5. e. The percentage of finishers with times less than 75 minutes is equal to the area under the standard normal curve that lies to the ________ of ________.